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%I #10 Aug 22 2024 05:29:39
%S 0,10,317,1235,28898,120742,1411753,201095722,306312948,12306316582,
%T 32679761048,806327047899,9600042921304,172192972068022
%N a(n) is the smallest k such that the first n digits of Fibonacci(k) are the reverse of its last n digits.
%C (Inspired by _D. S. McNeil_'s comment at A045504 that typically a Fibonacci number can be ruled out as a possible palindrome by checking only a few digits at the start and end of the number.)
%H Kevin Ryde, <a href="/A372729/a372729.c.txt">C Code</a>
%e a(1) = 0 (as Fibonacci(0) = 0 is the smallest Fibonacci number).
%e a(2) = 10 (Fibonacci(10) = 55 is the only 2-digit Fibonacci number that is palindromic, and almost certainly the only multidigit palindromic Fibonacci number; see A045504).
%e a(3) = 317 because Fibonacci(317) (a 66-digit number) is the smallest Fibonacci number whose first 3 digits (793) are the reverse of its last 3 digits (397).
%e The table below lists the first 8 terms and the corresponding Fibonacci numbers (abbreviated, for n > 2):
%e .
%e n a(n) Fibonacci(a(n))
%e - --------- -------------------
%e 1 0 0
%e 2 10 55
%e 3 317 793...397
%e 4 1235 5626...6265
%e 5 28898 94480...08449
%e 6 120742 172255...552271
%e 7 1411753 3789665...5669873
%e 8 201095722 11367389...98376311
%o (C) /* See links. */
%Y Cf. A000045, A002113, A045504.
%K nonn,base,hard,more
%O 1,2
%A _Jon E. Schoenfield_, May 11 2024
%E a(9)-a(14) from _Kevin Ryde_, Aug 22 2024
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